isSymType

Determine whether symbolic object is specific type

Syntax

TF = isSymType(symObj,type)

TF = isSymType(symObj,funType,vars)

Description

TF = isSymType(symObj,type) returns logical 1 (true) if the symbolic object symObj is of type type, and logical 0 (false) otherwise. The input type must be a case-sensitive string scalar or character vector, and it can include a logical expression. For example, isSymType(sym('3'),'real & integer') returns logical 1.

If symObj is a symbolic expression with a topmost operator of type type, then isSymType(symObj,type) also returns logical 1.

TF = isSymType(symObj,funType,vars) checks whether symObj is an unassigned symbolic function that depends on the symbolic variables vars.

You can set the function type funType to 'symfunOf' or 'symfunDependingOn'. For example, syms f(x); isSymType(f,'symfunOf',x) returns logical 1.

Examples

Symbolic Number and Constant

Create a symbolic number. Check whether the symbolic number is of type 'rational'.

a = sym('1/2');
TF = isSymType(a,'rational')

TF = logical
   1

Now construct a symbolic array by including symbolic numbers or constants in the array elements.

N = [sym('1/2'), vpa(0.5), pi, vpa(pi), 1i]

N = 
$$\left(\begin{array}{ccccc}\frac{1}{2}& 0.5& \pi & 3.1415926535897932384626433832795& \mathrm{i}\end{array}\right)$$

Check whether each array element is of type 'real'.

TF = isSymType(N,'real')

TF = 1x5 logical array

   1   1   0   1   0

Check whether each array element is of type 'integer | real'.

TF = isSymType(N,'integer | real')

TF = 1x5 logical array

   1   1   0   1   0

Check whether each array element is of type 'number'.

TF = isSymType(N,'number')

TF = 1x5 logical array

   1   1   0   1   1

Check whether each array element is of type 'constant'.

TF = isSymType(N,'constant')

TF = 1x5 logical array

   1   1   1   1   1

Topmost Operator of Symbolic Expression

Determine whether the topmost operator of a symbolic expression is of a specific type, such as 'plus' or 'power'.

Create a symbolic expression.

syms x
expr = x^2 + 2*x - 1

expr = $$x^2+2\hspace{0.17em}x-1$$

Check whether the topmost operator of expr is of type 'plus'.

TF = isSymType(expr,'plus')

TF = logical
   1

Check whether the topmost operator of expr is of type 'power'.

TF = isSymType(expr,'power')

TF = logical
   0

Now perform a symbolic square root operation in the expression.

expr = sqrt(x^2 + 2*x - 1)

expr = $$\sqrt{x^2+2\hspace{0.17em}x-1}$$

Check whether the topmost operator of expr is of type 'power'.

TF = isSymType(expr,'power')

TF = logical
   1

Select Specific Equations

Select specific equations that are constant on the right side.

Create an array of three symbolic equations.

syms r(t) x(t) y(t)
eq1 = [x(t) == r(t)*cos(t), y(t) == r(t)*sin(t), r(t) == 5]

eq1 = $$\left(\begin{array}{ccc}x\left(t\right)=\cos \left(t\right)\hspace{0.17em}r\left(t\right)& y\left(t\right)=r\left(t\right)\hspace{0.17em}\sin \left(t\right)& r\left(t\right)=5\end{array}\right)$$

Select the right side of each equation using the rhs function. Check whether the right side of each equation is of type 'constant'.

TF = isSymType(rhs(eq1),'constant')

TF = 1x3 logical array

   0   0   1

Return the reduced equation that is constant on the right side.

eq2 = eq1(TF)

eq2 = $$r\left(t\right)=5$$

Symbolic Function of Multiple Variables

Create a symbolic function of multiple variables f(x,y) using syms. Check whether the unassigned symbolic function f is of type 'symfun'.

syms f(x,y)
TF = isSymType(f,'symfun')

TF = logical
   1

Check whether f depends on the exact variable x.

TF = isSymType(f,'symfunOf',x)

TF = logical
   0

Check whether f depends on the exact sequence of variables [x y].

TF = isSymType(f,'symfunOf',[x y])

TF = logical
   1

Check whether f depends on the variable x.

TF = isSymType(f,'symfunDependingOn',x)

TF = logical
   1

Input Arguments

symObj — Symbolic objects

symbolic expressions | symbolic functions | symbolic variables | symbolic numbers | symbolic units

Symbolic objects, specified as symbolic expressions, symbolic functions, symbolic variables, symbolic numbers, or symbolic units.

type — Symbolic types

scalar string | character vector

Symbolic types, specified as a case-sensitive scalar string or character vector. The input type can contain a logical expression. The value options follow.

Symbolic Type Category	String Values	Examples Returning Logical 1
numbers	'integer' — integer numbers 'rational' — rational numbers 'vpareal' — variable-precision floating-point real numbers 'complex' — complex numbers 'real' — real numbers, including 'integer', 'rational', and 'vpareal' 'number' — numbers, including 'integer', 'rational', 'vpareal', 'complex', and 'real'	isSymType(sym(2),'integer') isSymType(sym(1/2),'rational') isSymType(vpa(0.5),'vpareal') isSymType(vpa(1i),'complex') isSymType([sym(1/2) vpa(0.5)],'real') isSymType([vpa(1i) sym(1/2)],'number')
constants	'constant' — symbolic mathematical constants, including 'number'	isSymType([sym(pi) vpa(1i)],'constant')
symbolic math functions	'vpa', 'sin', 'exp', and so on — topmost symbolic math functions in symbolic expressions	isSymType(vpa(sym(pi)),'vpa')
unassigned symbolic functions	'F', 'g', and so on — function name of an unassigned symbolic function 'symfun' — unassigned symbolic functions	syms F(x); isSymType(F(x+2),'F') syms g(x); isSymType(g(x),'symfun')
arithmetic operators	'plus' — addition operator + and subtraction operator - 'times' — multiplication operator * and division operator / 'power' — power or exponentiation operator ^ and square root operator sqrt	syms x y; isSymType(2*x + y,'plus') syms x y; isSymType(x*y,'times') syms x y; isSymType(x^(y+2),'power')
variables	'variable' — symbolic variables	isSymType(sym('x'),'variable')
units	'unit' — symbolic units	isSymType(symunit('m'),'unit')
expressions	'expression' — symbolic expressions, including all of the preceding symbolic types	isSymType(sym('x')+1,'expression')
logical expressions	'or' — logical OR operator | 'and' — logical AND operator & 'not' — logical NOT operator ~ 'xor' — logical exclusive-OR operator xor 'logicalconstant' — symbolic logical constants symtrue and symfalse 'logicalexpression' — logical expressions, including 'or', 'and', 'not', 'xor', symtrue and symfalse	syms x y; isSymType(x|y,'or') syms x y; isSymType(x&y,'and') syms x; isSymType(~x,'not') syms x y; isSymType(xor(x,y),'xor') isSymType(symtrue,'logicalconstant') syms x y; isSymType(~x|y,'logicalexpression')
equations and inequalities	'eq' — equality operator == 'ne' — inequality operator ~= 'lt' — less-than operator < or greater-than operator > 'le' — less-than-or-equal-to operator <= or greater-than-or-equal-to operator >= 'equation' — symbolic equations and inequalities, including 'eq', 'ne', 'lt', and 'le'	syms x; isSymType(x==2,'eq') syms x; isSymType(x~=1,'ne') syms x; isSymType(x>0,'lt') syms x; isSymType(x<=2,'le') syms x; isSymType([x>0 x~=1],'equation')
unsupported symbolic types	'unsupported' — unsupported symbolic types

funType — Function type

'symfunOf' | 'symfunDependingOn'

Function type, specified as 'symfunOf' or 'symfunDependingOn'.

• 'symfunOf' checks whether symObj is an unassigned symbolic function that depends on the exact sequence of variables specified by the array vars. For example, syms f(x,y); isSymType(f,'symfunOf',[x y]) returns logical 1.

• 'symfunDependingOn' checks whether symObj is an unassigned symbolic function that depends on the variables specified by the array vars. For example, syms f(x,y); isSymType(f,'symfunDependingOn',x) returns logical 1.

vars — Input variables

symbolic variables | symbolic array

Input variables, specified as symbolic variables or a symbolic array.